An efficient Peaceman–Rachford splitting method for constrained TGV-shearlet-based MRI reconstruction

ABSTRACT As a fundamental application of compressive sensing, magnetic resonance imaging (MRI) can be efficiently achievable by exploiting fewer k-space measurements. In this paper, we propose a constrained total generalized variation and shearlet transform-based model for MRI reconstruction, which is usually more undemanding and practical to identify appropriate tradeoffs than its unconstrained counterpart. The proposed model can be facilely and efficiently solved by the strictly contractive Peaceman–Rachford splitting method, which generally outperforms some state-of-the-art algorithms when solving separable convex programming. Numerical simulations demonstrate that the sharp edges and grainy details in magnetic resonance images can be well reconstructed from the under-sampling data.